Spring Semester 2015

Introduction to Partial Differential Equations

Syllabus

Quick Links:

Class mailing list for announcements and discussion
Homework sheets
Class handouts, exams, solutions

Summary:

This class is an introduction to the theory of partial differential equations. The main topics are: classification of PDEs, linear prototypes (transport equation, Poisson equation, heat equation, wave equation); functional setting, function spaces, variational methods, weak and strong solutions; examples of nonlinear parabolic PDEs, introduction to conservation laws; exact solution techniques, transform methods, power series solutions, asymptotics.

Contact Information:

Instructor:	Marcel Oliver
Email:	m.oliver@jacobs-university.de
Phone:	200-3212
Office hours:	Tu/Th 10:00-11:00 in Research I, 107

Time and Place:

Lectures:

Mo 9:45, We 8:15 in West Hall 4

Recommended Textbook:

L.C. Evans: Partial Differential Equations

Grading:

The final grade will be computed as a grade point average with the following weights:

Homework: 20%

Presentation: 10%

Midterm Exam: 30%

Final Exam: 40%
Each participant will give an approximately half-hour presentation toward the end of the semester. A topic should be chosen until April 1.
Each of the individual scores will be converted to Jacobs grade points before the overall weighted grade point average is computed.

Class Schedule (subject to change!)

Mon, 2. Feb. 2015:	Introduction; linear transport equation
Wed, 4. Feb. 2015:	Laplace equation, fundamental solution
Mon, 9. Feb. 2015:	Poisson equation, mean value formulas
Wed, 11. Feb. 2015:	Harmonic functions: maximum principle, uniqueness for solutions to the Poisson equation,
Mon, 16. Feb. 2015:	Harmonic functions: smoothness, estimates on derivatives, comment on analyticity, Liouville theorem with consequences
Wed, 18. Feb. 2015:	Harnack inequality; Dirichlet problem, Green's functions
Mon, 23. Feb. 2015:	Green's function for the half-space (ctd.); energy methods
Wed, 25. Feb. 2015:	Heat equation: introduction, fundamental solution, solution formulas
Mon, 2. Mar. 2015:	Initial value problem for the heat equation
Wed, 4. Mar. 2015:	Maximum principle, uniqueness
Mon, 9. Mar. 2015:	Energy methods for the heat equation
Wed, 11. Mar. 2015:	Wave equation: introduction and d'Alembert's formula for the wave equation in one spatial dimension
Mon, 16. Mar. 2015:	Wave equations in several dimensions; energy methods
Wed, 18. Mar. 2015:	Review for midterm exam
Mon, 23. Mar. 2015:	Midterm exam
Wed, 25. Mar. 2015:	First order equations, generalized characteristics
Wed, 8. Apr. 2015:	Scalar conservation laws, shock condition, entropy condition for piecewise smooth solutions
Mon, 13. Apr. 2015:	Introduction to Hamilton-Jacobi equations, Legendre transform
Wed, 15. Apr. 2015:	Discussion of Midterm exam
Mon, 20. Apr. 2015:	No class
Wed, 22. Apr. 2015:	Hopf-Lax formula, semiconcavity
Mon, 27. Apr. 2015:	Lax-Oleinik formula for scalar conservation laws, entropy condition
Wed, 29. Apr. 2015:	Riemann problem; Student presentation
Mon, 4. May 2015:	Review for final exam
Wed, 6. May 2015:	Final Exam, West Hall 1, 8:15-10:15
Mon, 11. May 2015:	Student presentations
Wed, 13. May 2015:	Student presentations
Wed, 20. May 2015:	Student presentations, West Hall 4, 15:00-19:00

Last modified: 2015/02/02
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/spring2015/math362/index.html
Marcel Oliver (m.oliver@jacobs-university.de)

Homework:	20%
Presentation:	10%
Midterm Exam:	30%
Final Exam:	40%